Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with respect to THB-splines, so that the coarser geometry approximates the initial geometry with a given level of the precision and is regular. The algorithm is based on the unrefinement of cells of the parameter domain, on which the geometry is defined, thus obtaining the new subdivision of the domain (the new subdomain hierarchy). The algorithm uses local linear projectors and optimization techniques in order to ensure the regularity and the approximation properties.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).